Question

x^2-4xy+3y^2因式分解

还有（ax^2y^2-a)÷(xy+1)
【（a-2b)^2-4(a-2b)+4】÷（a-2b-2)
m^4-2(m^2-1/2)

Answer 1

1.x²-4xy+3y²，用十字相乘法
=(x-3y)(x-y)

2.(ax²y²-a)/(xy+1)
=a[(xy)²-1]/(xy+1)
=a(xy+1)(xy-1)/(xy+1)，约掉公因数xy+1
=a(xy-1)

3.[(a-2b)²-4(a-2b)+4]/(a-2b-2)
=[(a-2b)-2]²/(a-2b-2)，约掉其中一个公因数a-2b-2
=a-2b-2

4.m^4-2(m²-1/2)
=m^4-2m²+1
=(m²-1)²
=(m+1)²(m-1)²

Answer 2

原式=x^2-(4y+1)x+3y^2-y-2(a^2+b^2-c^2-2ab)/(a-b-c)
=[(a-b)^2-c^2]/(a-b-c)
=(a-b+c)(a-b-c)/(a-b-c)
=a-b+c

(x^2-6x)^2+18(x^2-6x)+81=0
[(x^2-6x)+9]^2=0
(x^2-6x+9)^2=0
x^2-6x+9=0
(x-3)^2=0
x-3=0
x=3

(ax^2y^2-a)/(xy+1)
=a(x^2y^2-1)/(xy+1)
=a(xy+1)(xy-1)/(xy+1)
=a(xy-1)
=axy-a
=x^2-(4y+1)x+(y-1)(3y+2)
=(x-y+1)(x-3y+2)